Based on the differential quadrature (DQ) method, a new algorithm for the instability analysis of fluid and elastic panel system is presented in this paper. The governing equations of both subsonic compressible airflow and two-dimensional elastic panel are discretized using the differential quadrature method at the same grid points. The coupled fluid-panel equation is analyzed by using eigenvalue theory and the instability characteristics of panels with differential boundary conditions are given. The results show: the elastic panel which is simply support or clamped at both ends undergoes divergence but not flutter; this algorithm has the advantages of producing highly accurate solutions with minimal computational effort.